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Simplifying (9 + 9i)(9 + i) = 0 Multiply (9 + 9i) * (9 + i) (9(9 + i) + 9i * (9 + i)) = 0 ((9 * 9 + i * 9) + 9i * (9 + i)) = 0 ((81 + 9i) + 9i * (9 + i)) = 0 (81 + 9i + (9 * 9i + i * 9i)) = 0 (81 + 9i + (81i + 9i2)) = 0 Combine like terms: 9i + 81i = 90i (81 + 90i + 9i2) = 0 Solving 81 + 90i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9'. 9(9 + 10i + i2) = 0 Factor a trinomial. 9((9 + i)(1 + i)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-9, -1}
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